Project Overview¶

Goal: Construct a model that accurately predicts whether an individual makes more than 50k/yr
Motivation: Help a non-profit identify donor candidates and understand how large of a donation to request
Data Source: 1994 US Census Data UCI Machine Learning Repository*

Note: Datset donated by Ron Kohavi and Barry Becker, from the article "Scaling Up the Accuracy of Naive-Bayes Classifiers: A Decision-Tree Hybrid". Small changes to the dataset have been made, such as removing the 'fnlwgt' feature and records with missing or ill-formatted entries.

Exploratory Data Analysis (EDA)¶

Featureset Exploration

age: continuous.
workclass: Private, Self-emp-not-inc, Self-emp-inc, Federal-gov, Local-gov, State-gov, Without-pay, Never-worked.
education: Bachelors, Some-college, 11th, HS-grad, Prof-school, Assoc-acdm, Assoc-voc, 9th, 7th-8th, 12th, Masters, 1st-4th, 10th, Doctorate, 5th-6th, Preschool.
education-num: continuous.
marital-status: Married-civ-spouse, Divorced, Never-married, Separated, Widowed, Married-spouse-absent, Married-AF-spouse.
occupation: Tech-support, Craft-repair, Other-service, Sales, Exec-managerial, Prof-specialty, Handlers-cleaners, Machine-op-inspct, Adm-clerical, Farming-fishing, Transport-moving, Priv-house-serv, Protective-serv, Armed-Forces.
relationship: Wife, Own-child, Husband, Not-in-family, Other-relative, Unmarried.
race: Black, White, Asian-Pac-Islander, Amer-Indian-Eskimo, Other.
sex: Female, Male.
capital-gain: continuous.
capital-loss: continuous.
hours-per-week: continuous.
native-country: United-States, Cambodia, England, Puerto-Rico, Canada, Germany, Outlying-US(Guam-USVI-etc), India, Japan, Greece, South, China, Cuba, Iran, Honduras, Philippines, Italy, Poland, Jamaica, Vietnam, Mexico, Portugal, Ireland, France, Dominican-Republic, Laos, Ecuador, Taiwan, Haiti, Columbia, Hungary, Guatemala, Nicaragua, Scotland, Thailand, Yugoslavia, El-Salvador, Trinadad&Tobago, Peru, Hong, Holand-Netherlands.

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 45222 entries, 0 to 45221
Data columns (total 14 columns):
 #   Column           Non-Null Count  Dtype  
---  ------           --------------  -----  
 0   age              45222 non-null  int64  
 1   workclass        45222 non-null  object 
 2   education_level  45222 non-null  object 
 3   education-num    45222 non-null  float64
 4   marital-status   45222 non-null  object 
 5   occupation       45222 non-null  object 
 6   relationship     45222 non-null  object 
 7   race             45222 non-null  object 
 8   sex              45222 non-null  object 
 9   capital-gain     45222 non-null  float64
 10  capital-loss     45222 non-null  float64
 11  hours-per-week   45222 non-null  float64
 12  native-country   45222 non-null  object 
 13  income           45222 non-null  object 
dtypes: float64(4), int64(1), object(9)
memory usage: 4.8+ MB

Number of observations: 45222
Number of people with income > 50k: 11208
Number of people with income <= 50k: 34014
Percent of people with income > 50k: 24.78

Data Preprocessing ¶

Before this data can be used for modeling and application to machine learning algorithms, it must be cleaned, formatted, and structured.

Split the data into features and labels

Skew¶

The features capital-gain and capital-loss are positively skewed (i.e. have a long tail in the positive direction).

To reduce this skew, a logarithmic transformation, $\tilde x = \ln\left(x\right)$, can be applied. This transformation will reduce the amount of variance and pull the mean closer to the center of the distribution.

Why does this matter: The sample being observed may be a poor aproximation of the population.

Asymptotic normality indicates that a sample will approach a normal distribution even if the population is skewed.

As per the central limit theorem, as the sample size (the number of means, i.e. the number of samples) increases, $n\rightarrow \infty$, the sampling distribution of the means will become more normally distributed even though the population distribution is skewed.
When $n$ is large, asymptotic theory provides us with a more complete picture of the “accuracy” of $\lambda$: By the Law of Large Numbers, $\bar{X}$ converges to $\lambda$ in probability as $n \rightarrow \infty$. Furthermore, by the Central Limit Theorem, $$n(\bar{X} − \lambda) \rightarrow N (0, Var[X_{i}]) = N (0, \lambda)$$ in distribution as $n \rightarrow \infty$. So for large $n$, we expect $\hat{\lambda}$ to be close to $\lambda$, and the sampling distribution of $\hat{\lambda}$ is approximately $N\left(\lambda, \frac{\lambda}{n}\right)$

Apply the logarithmic transformation:¶

The logarithmic transformation reduced the skew and the variance of each factor.¶

Feature	Skewness	Mean	Variance
Capital Loss	4.516154	88.595418	163985.81018
Capital Gain	11.788611	1101.430344	56345246.60482
Log Capital Loss	4.271053	0.355489	2.54688
Log Capital Gain	3.082284	0.740759	6.08362

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	count	unique	top	freq	mean	std	min	25%	50%	75%	max
age	45222	NaN	NaN	NaN	38.5479	13.2179	17	28	37	47	90
workclass	45222	7	Private	33307	NaN	NaN	NaN	NaN	NaN	NaN	NaN
education_level	45222	16	HS-grad	14783	NaN	NaN	NaN	NaN	NaN	NaN	NaN
education-num	45222	NaN	NaN	NaN	10.1185	2.55288	1	9	10	13	16
marital-status	45222	7	Married-civ-spouse	21055	NaN	NaN	NaN	NaN	NaN	NaN	NaN
occupation	45222	14	Craft-repair	6020	NaN	NaN	NaN	NaN	NaN	NaN	NaN
relationship	45222	6	Husband	18666	NaN	NaN	NaN	NaN	NaN	NaN	NaN
race	45222	5	White	38903	NaN	NaN	NaN	NaN	NaN	NaN	NaN
sex	45222	2	Male	30527	NaN	NaN	NaN	NaN	NaN	NaN	NaN
capital-gain	45222	NaN	NaN	NaN	1101.43	7506.43	0	0	0	0	99999
capital-loss	45222	NaN	NaN	NaN	88.5954	404.956	0	0	0	0	4356
hours-per-week	45222	NaN	NaN	NaN	40.938	12.0075	1	40	40	45	99
native-country	45222	41	United-States	41292	NaN	NaN	NaN	NaN	NaN	NaN	NaN
income	45222	2	<=50K	34014	NaN	NaN	NaN	NaN	NaN	NaN	NaN